I think it would make more sense to have origin specific mage skills. A mage from Tevinter might have some different skills than a mage that was trained in a southern Circle, and those two formally trained mages might have different skills from someone like Morrigan that was not formally trained, but all three of these are human. They in turn might have different skills from a Dalish mage, a Vashoth mage, or a Qunari Saarebas.
Lore and party banter supports this.
Vivienne, Dorian and Solas all have their own unique style when it comes to casting magic according to Bull, who pointedly comments that he cannot figure out why Solas doesn't have something that "clunks" in his style as the others do.
Several bits of banter between Dorian and Solas are on how similar their styles are and how they both use similar means to get more "kick" out of spells. Solas claims this is because Tevinter magic was heavily influenced by - and appropriated from - the Ancient Elves and their schools of thought when the Imperium conquered them.
Likewise, VIvienne repeatedly derides Solas' skill and assumes he is incompetent because he was not "properly" trained in a Circle as she was.
This even shows up back in Origins, where Flemeth similarly tells a Mage Warden that her methods are so different from how the Circle teaches it's students, they would have to spend years learning her ways in order to have any hope of performing magic as she does.
(On a somewhat related note, can Elves and Dwarves demonstrate superior night-vision at some point in the series? The lore supposedly says that they should have this ability compared to humans, so it'd be a nice little detail to throw in.)